572 



BELL SYSTEM TECHNICAL JOURNAL 



These four cases will be de\-eloped in detail and eqiii\aleni-e relations 

 for certain sets of terminal combinations shown. 



Fundamculal Formula 



The formula which is general and fundamental to wiial follows is 

 the one giving the current received through a passive transducer in 

 terms of the sending electromotive force, the terminal imfjedances. 



1 '» 



Vb 



Fig. .3 — General Linear TransiJucer 



and the transfer constant' and image impedances of the transducer. 

 F^eferred to Fig. 3 the received current is 



/6 = 



2Ea VWaWb e-T 



(Wa+Z,) (fn+Zi) (1 -r„r6e-"-) 



(3) 



/Jo = sending electromotive force, 



Za, Z(, = sending and recei\ing impedances, 



7' = Z) + !5= transfer constant of the transducer, 



/?, .S = diminution constant and angular constant, defined as 

 the real and imaginary parts of the transfer constant. 



H'l, TI'i, = image impedances of the transducer at terminals </ and !>> 



''o, ^6 = current reflection coefficients at terminals a and b, 



Wa-Za 



and 



rb = 



^Va+Za 



Wb-Zt 

 Wb+Zb 



' The terms transfer constant, T and image impedances, \V„ and \\\, as applied 

 to a dissyninielrical passive transducer, are defined in the Appendix. These three 

 parameters are to be distinguished from another set, the propagation constant, 1', 

 and characteristic impedances, A'„ and A'j. In a symmetrical structure r=r and 



